Math 8 Semester 2 Review
Topics to know (and love): Midpoint/Distance, Probability, Functions, Rate of Change, Linear EQs, SA/Volume
Show all work in a neat and organized manner on separate paper.
Midpoint/Distance Review
1 (a) Plot quadrilateral TIGR on the coordinate system below. (use graph paper)
T (-8,8)
I (-5, -2)
G(5,0)
R(2,10)
(b) Find the following distances. Show work.
Length of segment TR
Length of segment RG
Length of segment GI
Length of segment IT
(c) Which if any of the above segments are equal?
What does this tell you about quadrilateral TIGR?
Find the midpoints for the following sets of points:
2. (-3, 2) and (7, -2)
3. (0, 0) and (5, 2)
4. (12, 3) and (-12, -5)
Find the lengths and slopes of each side of the triangle; then classify the triangle.
5. A (-3, 1)
B (2, -5)
C (4, 6)
Find the missing endpoints when given the midpoint and an endpoint:
6. Endpoint: (4, 9) and Midpoint: (‒2, 5)
7. Endpoint: (‒3, 10) and Midpoint: (17, ‒5)
Probability Review: Remember to show your work! (set up and steps)
7. The six faces of a fair cube are numbered 1 to 6. If the cube is rolled 300 times, what is the expected
number of times a 3 will land face up?
8. The diagram below shows a spinner. The pointer is spun, and the player is awarded a prize according
to the color on which the
pointer stops.
a. What is the probability that the pointer stops in the red region?
b. Complete the table below showing the probabilities of the three possible results.
Color
Red Green Blue
Probability
c. Find the probability that the pointer stops on green or blue.
d. Find the probability that the pointer does not stop on green.
9.
10.
11.
12. A restaurant owner wants to let his customers know how many different bagel choices the restaurant
offers. Bagels come in small, medium or large. There are nine different flavors of bagels and you can
have them sliced or not sliced. Determine how many bagel combinations the restaurant offers.
13. John’s movie theatre offers the following choices for snacks: Popcorn, candy, or nachos, in small
medium or large, with or without a drink. Which of the following shows the total number of snack
combinations available at John’s movie theatre?
A
3+3+2
B
3321
C
3+3
D
332
14.
a. Draw a tree diagram to display the number of possible outcomes of a spinner with 3 equal parts that
are colored RED, BLUE and YELLOW and then rolling a 6 sided number cube. (Record the
outcomes like RED- 2 for spinning a red and rolling a 2.)
b. What is the probability of spinning a Yellow and then rolling a 3 or a 4?
c. What is the probability of rolling a 1 and spinning a RED?
15.
16.
17 & 18
17.
18.
19.
20.
21.
Determine if each is a permutation or combination. Do NOT solve.
22. In how many ways can a committee of 3 be selected from a class of 8 students?
23. In how many ways can a President and Vice President be selected from a pool of 6 people?
24. A political science professor must select 4 students from her class of 12 students for a field trip to state
legislature. In how many ways can she do it?
25. The professor was asked to rank the top 4 students in her class of 12. In how many ways can that be done?
26. A police chiefs needs to assign officers from the 10 available to control traffic at intersections A, B, and C. In
how many ways can he do it?
Evaluate each combination or permutation: (show work as always!)
27. If 12 horses are entered in a race, how many ways can the first 3 places be awarded?
28. A 4-digit PIN for the ATM must be created. How many different PIN’s can be formed if digits can be
repeated?
29. How many 4 person committees could be created from a selection of 14 people?
30. How many different arrangements can be made from the letters in the word CHAIR if none of the letters
repeat.
31. How many ways are there to choose 2 sides from a menu with 12 options?
Functions:
1. This November, FFA students are making fruit baskets to sell to the community to raise money for a
trip. Cassie, an FFA student, is able to make 10 fruit baskets and will sell them for $40 each.
Domain;
Range:
Choose one: Discrete or Continuous
Choose one: Relation or Function
2. {(1, 8), (2, 11), (3, 14), (4, 17), (5, 20), (6, 23)}
Domain; Range:
Choose one: Discrete or Continuous
3.
Domain:
Range:
Choose one: Discrete or Continuous
Input
-3
-1
1
3
5
Output
-5.25
-3.25
-1.25
0.75
2.75
Choose one: Relation or Function
4.
Domain;
Range:
Choose one: Discrete or Continuous
Choose one: Relation or Function
5. The equation M = 4.4n, relates the number of quarters, n, to its mass, M, in grams. What is the
independent variable?
A).
B).
C).
D).
The mass of the quarters.
The value of the quarters.
The number of quarters.
Each quarter weighs 4.4 grams.
6. Which set of ordered pairs represents a function?
A).
B).
C).
D).
{ (1,1) (1,– 1) ( 4, 2) (4, –2) (9, 3) }
{ (3, 4) (3, 5) (3, 6) (3, 7) (3, 8) }
{ (2, 4) (3, 4) (4, 4,) (5, 4) (6,4) }
{ (1, 2) (2, 3) (3,4) (4,5) (4, 6) }
7. Given the rule, complete each function machine:
n6
a)
2
3
1
5
6
0
8.
)
2
3
1
5
6
0
2n
c)
2n  3
2
3
1
5
6
0
Determine whether each of the following relations is a function. Justify answer.
9.
Given the functions below, evaluate each of the following. Show all work!!
𝒇(𝒙) = 𝟑𝒙 + 𝟐
i.
v.
10.
𝒈(𝒙) = 𝒙𝟐 – 𝒙
𝑓(4)
ii.
ℎ(𝑥) = 7
vi.
𝑔(5)
𝑓(𝑥) = ‒ 7
𝒉(𝒙) = 𝟒𝒙 − 𝟏
iii. ℎ(−3)
vii.
iv. 𝑔(−2)
ℎ(𝑥) = 5
Sunflower Seeds Graphs
Ian and his friends are sitting around eating sunflower seeds. Each person had a bowl with the same
amount of seeds. The graphs show the amount of sunflower seeds remaining in the person’s bowl
over a period of time.
Write sentences that describe what may have happened for each person.
11.
Complete the following questions using the graph shown.
a)
What is the independent variable?
b)
What is the dependent variable?
c)
Name the ordered pair for point C and explain what it
represents.
d)
Name the ordered pair for point D and explain what it
represents.
12.
A bird sitting on a tree flies away, then returns to the tree. His altitude over time
is graphed below:
a. During which stage(s) of the flight was
the altitude increasing? ______________
b. During which stage(s) of the flight was
the altitude decreasing? ______________
3
Altitude (feet)
4
c. What is happening to the altitude in stage
2? ___________________________
2
d. How tall is the tree the bird was sitting
on? ________________
1
Time (minutes)
e. What is the highest altitude the bird flew?
_________________
6. What is the domain of the situation
above? _____________________________
Rates of Change:
1. List the other names for rate of change.
7. What is the range of the situation above?
________________________________
2. Find the rate of change for the following tables and write the equation of each line in intercept form.
x
y
0
2
1
7
2
12
3
17
x
y
x
y
x
y
-2
10
-2
-6.5
3
6
1
1
0
-6
5
10
4
-8
3
-5.25
-1
-2
6
-14
6
-4.5
7
14
3.
Use the graph below describing Mary’s bike ride to answer the questions.
Distance in Miles (Y)
8
5
6
4
5
4
3
3
2
2
1
1
0
a).
2
1
3
5
4
Time in Minutes
6
8
What is the domain?
a.
b.
c.
d.
The distance is from 0 to 6 miles.
The time is from 0 to 8.5 minutes.
The time is from 0 to 6 minutes.
The distance is from 0 to 8 miles.
d).
What does
e).
For segment
a.
1
represent? ________________
2
:
How far did Mary ride?
3
b.How long did it take Mary? ___________
f).
For segment
i).
In which segment is Mary traveling the fastest?
a.
j).
7
, what is going on: __________________
How do you know?
During which interval is Mary traveling the slowest?
4.
Find the slope of the line from the graphs and write the equation of each line in intercept form.
a.
b.
c.
Special Lines and Their Slopes
5. Find the rate of
change
x
y
0
5
1
5
2
5
3
5
Graph the points.
What kind of line is this?
Write the equation of the line.
_________________ lines have a slope of ____________________ and the equations look like ____________
Here’s how I will remember this:
6. Find the rate of
x
y
-2
-3
-2
0
-2
2
-2
5
Graph the points.
change
What kind of line is this?
Write the equation of the line.
_________________ lines have an _______________________slope and the equations look like ___________
Here’s how I will remember this:
Linear Equations:
1.
2.
For each graph: Write the equation of the line in SLOPE-INTERCEPT FORM
Determine the slope and y-intercept of the following:
𝑎) 𝑦 = 4𝑥 – 5
b)
y
2
x
3
3. Find the equation of the line in slope-intercept form (y = mx + b)
a) Slope of 2 and y-intercept of -7
b) y-intercept of = 4 and m = -5
c) Slope = 3/5 and (0, -2).
d) m = -4/7 through (14, 3)
e) Between (5, 6) and (-3, 8)
f) Through (‒4, 7) and (2, 5)
Write the slope of the line that is PARALLEL to each line.
5.
4y
 2x  5
6.
y  x  2
7.
y
3
x7
4
y
3
x7
4
Write the slope of the line that is PERPENDICULAR to each line.
8.
6y
 2x  5
9.
2y
 x  2
10.
11.
Write an equation in Slope-Intercept form of the line that is parallel to y = 5x + 12 and
contains the point ( 2, –3 ).
12.
Write an equation in Slope-Intercept form of the line that is perpendicular to y = 3x – 22
and contains the point ( 6, 2 ).
Graph the following neatly on graph
13.
3x – 4y = ‒6
14.
paper.
20 – 5y = 10x
15.
y = 3x + 5
16.
10y = ‒2x + 15
Find the x and y intercepts of the following:
17.
2𝑥 − 3𝑦 = 14
18. X = 8
19. 𝑦 = 5𝑥 − 10
20. Convert words to equations and inequalities.
a) “Six less than a number is twice the number.”
b) “The product of four and a number is the sum of the number and twelve.”
21. Write equations to solve word problems. Define variables and write an equation but do not
solve.
a) A plumber’s bill is $350 dollars for 3 hours of works. If the bill includes $110 for parts, write an
equation to find his hourly rate.
b) Candice has lost 6 pounds by eating less sugar and exercising each day. If she continues to
lose 1.5 pounds per week, write an equation for her weight loss in terms of the number of weeks
she continues this practice.
22. Graphic Design Charges – OE